Two things need to be understood about the Britt list. The first is that he wasn't writing about Fascism but instead about proto-fascism.

Second is that the Britt list presented by Rense.com is actually a fake. Rense is Jeff Rense's site, who back in the early 2000's was a prominent radio host and conspiracy theorist. He was a collaborator of Alex Jones until they had a falling out. Rense's site is know for anti-semitism and holocaust denial.

The "Dr. Britt" version of the list is the fake and it appears everywhere on the internet. It was a rewritten version of Britt's article that appeared in Free Inquiry Magazine.

From what I can tell, this is the mostly complete version of the article still online. The Fake List uses the general points but drops or rewrites all the qualifying statements. The real Britt cites several sources for his article.

So the real Britt was not writing about "defining characteristics" of fascism. He was writing about proto-fascism, meaning regimes that mimicked fascist imagery but not really fascist policies. He explicitly notes that:

Although many scholars question any direct connection among these regimes, few can dispute their visual similarities.

He's directly pointing out that most of the regimes (Portugal, Greece, Chile, Indonesia) he's writing about are not related to fascism at all. So he's really writing about vague characteristics of dictatorships. With Britt's vague list, some Communist regimes can be identified as Fascist regimes.

Eco does the exact same thing, and he acknowledges it throughout his article. He spends the first section pointing out the constant contradictions within the Fascist movement and the Fascist state. Then when he tries to find common characteristics, he explicitly states that they are typical features of despotism, not necessarily fascism.

But in spite of this fuzziness, I think it is possible to outline a list of features that are typical of what I would like to call Ur-Fascism, or Eternal Fascism. These features cannot be organized into a system; many of them contradict each other, and are also typical of other kinds of despotism or fanaticism. But it is enough that one of them be present to allow fascism to coagulate around it.

So both Britt and Eco directly, and repeatedly, acknowledged that they weren't really writing about fascism. They were basically writing about despotism or even authoritarianism.

Somehow people keep missing these points. If you read both articles with this in mind I think they are acceptable, but people in general keep trying to present them as "defining characteristics" of National Socialism and Italian Fascism. But if that were the case, some Fascist regimes like Spain or Vichy France would not meet those definitions of Fascism. At the same time, some Communist regimes can be identified as fascist if people keep reading these articles with that degree of vagueness.

The poster is something that comes from a Laurence Britt. While he is sometimes paraded around as a PhD, and/or expert on Fascism neither of these claims are backed up. He wrote "June" and does not himself claim to be either of those. So claims to his own authority are lacking merit. Snopes Goes into a bit more detail on his own arguments. However while he is not an expert we can still look at his definitions, and compare than to Umberto Eco's which to see perhaps some of the differences. I think at this point though it is important to note that the author also seems to have devised his criteria to attempt to appeal to modern day sensibilities rather than reflect on specific Fascist states, which themselves had a decent amount of variation in their ideologies.

Further defining any ideology/system is often extremely difficult. Political Science isn't really able to define 'Democracy' because there are many, many definitions and people make entire careers on writing about it. So there can easily be critiques of any definition of Fascism, and Eco looks far more at Italian Fascism than Franco or Hitler, which can make him overly specific. Britt on the other hand goes overly broad. So with that said lets begin comparing the two.

The first point I'm going to look at it is Britt's 'Rampant Sexism' claim. This contrasts nicely with Eco's description of Ur-Fascism containing an element of Machismo.

'This is the origin of machismo (which implies both disdain for women and intolerance and condemnation of nonstandard sexual habits, from chastity to homosexuality)'

While at first those two main seem quite similar, certainly having a disdain for women is sexist, the difference is in how one would apply this. Promotion of machismo has a broader point in Fascism, which is to allow the average man to experience their own heroism and obtain their self-worth this way. Britt's definition would apply to many cultures that are not Fascist themselves. Being overly broad, while helping with parsimony, in this case becomes mostly meaningless. Looking at the era in which Fascism arose, women barely had the right to vote, so claiming that Sexism was an indication of rising Fascism is not all that useful. When everyone is sexist, that some become Fascist needs a better explanation of why.

Having seen the failing of Britt when he's making the same point as Eco, I'd turn our attention to a point that is absent (essentially) in Eco, while present in Britt. 'Disdain for Intellectuals and the Arts.

That point is not borne out by history. Or more accurately that needs a major qualification that this applies to dissenters added. Nazi Germany certainly promoted art and artists that supported the regime, they had a ministry dedicated to doing that, and focused on purging dissenters rather than eliminating art and artists. As for thinkers we can look at the career of Carl Schmitt as perhaps quite emblematic of how Fascists approach the intellectuals. He initially received promotions and appointments for writing in support of the Nazi regime, and he is a major Fascist writer. However he eventually fell out of favor as he was deemed to have been to critical of the Nazis, and lost some of those positions for insufficient loyalty. So it is incorrect to say that hate of the arts or universities is indicative of Fascism, as they will certainly embrace both as long as it supports the regime.

Unfortunately including that qualifier to Britt makes the definition overly broad again, and we can easily see that Communist regimes fulfill that quite easily, and in fact fulfill most of his points of Fascism despite being very different ideologies.

Umberto gets to a similar point, that Fascists seek to suppress art and intellectuals who dissent, in a far longer, but ultimately stronger way. He notes that Fascism has a strong appeal to tradition, and anti-modernism, while also hating difference as well as using Newspeak, and selective, elitist populism. These points all combine to far better identify how Fascists treated artists who did not support the regime during the time, as art was good as long as it supported the eternal war against the enemies of the people, emphasized traditional values (as defined by the state) and would not have promoted to much thinking against the regime.

So then how does Eco stack up against other writers defining Fascism? Well as I mentioned earlier defining ideologies is something political science tends to struggle with, and Fascism is no exception. Hayek, Gentile, Mussolini, Schmitt, all also provide definitions, or theories/justifications of fascism. Hannah Arendt as well has also done a great deal, of highly respected work on both Fascism, and Totalitarianism (an even more difficult area).